ESupX1 = Compile[{{lF, _Integer}, {l\[Gamma], _Integer}, {x, _Real}, \
{y, _Real}, {z, _Real}, {t, _Real}},
   Module[{\[Theta] = .2,
     k = 2 Pi, \[Kappa] = k Sin[\[Theta]], \[Omega] = 1},
    Re[1/Sqrt[
      2] ((Exp[-I \[Omega] t] (I^-1 Exp[
              I (l\[Gamma]) ArcTan[x, y]] Cos[\[Theta]/2]^2 BesselJ[
              l\[Gamma], \[Kappa] Sqrt[x^2 + y^2]] (-(1/Sqrt[2])) +
            I^1 Exp[I (l\[Gamma] + 2) ArcTan[x, y]] Sin[\[Theta]/
              2]^2 BesselJ[
              l\[Gamma] + 2, \[Kappa] Sqrt[x^2 + y^2]] (1/Sqrt[
              2])) Exp[-0.5 z Sum[(Sqrt[\[Kappa]/(
                 2 Pi)] (BesselJ[
                   mf - l\[Gamma] -
                    1 , \[Kappa] Sqrt[x^2 + y^2]] (-1)^(
                  mf - 1) ((lF + mf)! (lF - mf)! (lF + 1)! (lF -
                    1)!)^.5 Sum[
                   If[kk >= 0 && (lF - mf - kk) >=
                    0 && (lF + 1 - kk) >= 0 && (mf - 1 + kk) >=
                    0, ((-1)^kk (Cos[\[Theta]/2])^(
                    2 lF - 2 kk - mf + 1) (Sin[\[Theta]/2])^(
                    2 kk + mf -
                    1))/(kk! (lF - mf - kk)! (lF + 1 - kk)! (mf - 1 +
                    kk)!), 0], {kk, -20,
                    20}]))^2, {mf, -lF, +lF}]/(2 Cos[\[Theta]] (\
\[Kappa] \[Omega]^2)/(
               4 Pi) (Cos[\[Theta]/2]^4 BesselJ[
                   l\[Gamma], \[Kappa] Sqrt[x^2 + y^2]]^2 +
                 Sin[\[Theta]/2]^4 BesselJ[
                   l\[Gamma] + 2, \[Kappa] Sqrt[x^2 + y^2]]^2 +
                 Sin[\[Theta]]^2/
                  2 BesselJ[
                   l\[Gamma] +
                    1, \[Kappa] Sqrt[
                    x^2 + y^2]]^2))]) + (-Exp[-I \[Omega] t] (I^1 Exp[
              I (l\[Gamma]) ArcTan[x, y]] Cos[\[Theta]/2]^2 BesselJ[
              l\[Gamma], \[Kappa]  Sqrt[x^2 + y^2]] (-(1/Sqrt[2])) +
            I^-1 Exp[I (l\[Gamma] - 2) ArcTan[x, y]] Sin[\[Theta]/
              2]^2 BesselJ[
              l\[Gamma] - 2, \[Kappa]  Sqrt[x^2 + y^2]] (1/Sqrt[
              2])) Exp[-0.5 z Sum[(Sqrt[\[Kappa]/(
                 2 Pi)] (BesselJ[
                   mf - l\[Gamma] +
                    1 , \[Kappa] Sqrt[x^2 + y^2]] (-1)^(
                  mf + 1) ((lF + mf)! (lF - mf)! (lF - 1)! (lF +
                    1)!)^.5 Sum[
                   If[kk >= 0 && (lF - mf - kk) >=
                    0 && (lF - 1 - kk) >= 0 && (mf + 1 + kk) >=
                    0, ((-1)^kk (Cos[\[Theta]/2])^(
                    2 lF - 2 kk - mf - 1) (Sin[\[Theta]/2])^(
                    2 kk + mf +
                    1))/(kk! (lF - mf - kk)! (lF - 1 - kk)! (mf + 1 +
                    kk)!), 0], {kk, -20,
                    20}]))^2, {mf, -lF, +lF}]/(2 Cos[\[Theta]] (\
\[Kappa] \[Omega]^2)/(
               4 Pi) (Cos[\[Theta]/2]^4 BesselJ[
                   l\[Gamma], \[Kappa] Sqrt[x^2 + y^2]]^2 +
                 Sin[\[Theta]/2]^4 BesselJ[
                   l\[Gamma] + 2, \[Kappa] Sqrt[x^2 + y^2]]^2 +
                 Sin[\[Theta]]^2/
                  2 BesselJ[
                   l\[Gamma] + 1, \[Kappa] Sqrt[x^2 + y^2]]^2))
           ]))]], CompilationTarget -> "C",
   RuntimeOptions -> "Speed", Parallelization -> True];